The subject matter of the present invention relates to a reservoir simulator including a parameter determination software which determines displacement parameters representing subsidence in an oilfield reservoir. More particularly, the present invention relates to methods for calculating the three dimensional stress field around a single or a series of geological faults, an equilibration technique that may be used to initiate the stresses and pore volumes, and methods to allow elastic or non-elastic change in rock pore volume to be coupled to the stress calculation that provide an alternative to more complex plastic failure models.
There are many recent reports of geomechanical modeling being used predictively for evaluation of alternative reservoir development plans. In the South Belridge field, Kern County, California, Hansen et al1 calibrated finite-element models of depletion-induced reservoir compaction and surface subsidence with observed measurements. The stress model was then used predictively to develop strategies to minimize additional subsidence and fissuring as well as to reduce axial compressive type casing damage. Berumen et al2 developed an overall geomechanical model of the Wilcox sands in the Arcabuz-Culebra field in the Burgos Basin, northern Mexico. This model, combined with hydraulic fracture mapping together with fracture and reservoir engineering studies, was used to optimize fracture treatment designs and improve the planning of well location and spacing.
The subject of fluid flow equations which are solved together with rock force balance equations has been discussed extensively in the literature. Kojic and Cheatham3,4 present a lucid treatment of the theory of plasticity of porous media with fluid flow. Both the elastic and plastic deformation of the porous medium containing a moving fluid is analyzed as a motion of a solid-fluid mixture. Corapcioglu and Bear5 present an early review of land subsidence modeling and then present a model of land subsidence as a result of pumping from an artesian aquifer.
Demirdzic et al6,7 have advocated the use of finite volume methods for numerical solution of the stress equations both in complex domains as well as for thermo-elastic-plastic problems.
A coupling of a conventional stress-analysis code with a standard finite difference reservoir simulator is outlined by Settari and Walters8. The term “partial coupling” is used because the rock stress and flow equations are solved separately for each time increment. Pressure and temperature changes as calculated in the reservoir simulator are passed to the geomechanical simulator. Updated strains and stresses are passed to the reservoir simulator which then computes porosity and permeability. Issues such as sand production, subsidence, compaction that influence rock mass conservation are handled in the stress-analysis code. This method will solve the problem as rigorously as a fully coupled (simultaneous) solution if iterated to full convergence. An explicit coupling, i.e. a single iteration of the stress model, is advocated for computational efficiency.
The use of a finite element stress simulator with a coupled fluid flow option is discussed by Heffer et al9 and by Gutierrez and Lewis10.
Standard commercial reservoir simulators use a single scalar parameter, the pore compressibility, as discussed by Geertsma11 to account for the pressure changes due to volumetric changes in the rock. These codes generally allow permeability to be modified as a function of pore pressure through a table. This approach is not adequate when the flow parameters exhibit a significant variation with rock stress. Holt12 found that for a weak sandstone, permeability reduction was more pronounced under non-hydrostatic applied stress, compared with the slight decrease measured under hydrostatic loading. Rhett and Teufel13 have shown a rapid decline in matrix permeability with increase in effective stress. Ferfera et al14 worked with a 20% porosity sandstone and found permeability reductions as high as 60% depending on the relative influence of the mean effective stress and the differential stress. Teufel et al15 and Teufel and Rhett16 found, contrary to the assumption that permeability will decrease with reservoir compaction and porosity reduction, that shear failure had a beneficial influence on production through an increase in the fracture density.
Finite element programs are in use that include a method to calculate the stress field around a fault or discontinuity in a porous medium. Similarly, stress equilibration techniques exist in software such as finite element programs. However, so far as is known, such programs cannot calculate the stress field around a fault or discontinuity in the presence of multi-phase (wherein the number of phases is between 1 and 3) flowing fluid with a full PVT description of each phase where the flowing fluid residual equations (fluid component conservation equations) are simultaneously solved with the rock stress equations (rock momentum conservation equations) and a residual equation describing rock volume or mass conservation.
Rock stress is a function of rock displacement. Rock displacement can be represented as rock strain, an example of which is set out below in equation (19). For infinitesimally small displacements, rock usually behaves elastically according to Hooke's law (see Fjaer, E., Holt, R. M., Horsrud, P. Arne, M. R., Risnes, R., “Petroleum Related Rock Mechanics,” Elsevier Science, Netherlands, 1992), which is a linear relation between rock stress and strain. However under a sufficient loading force, a rock may begin to fail. Failure includes phenomena such as cracking, crushing and crumbling. There are several models that represent this failure, the most common in soil mechanics being Mohr-Coulomb and Drucker-Praeger (Id.). These models are highly nonlinear and often difficult to compute. This phenomenon is called plasticity. Often the character of the material changes, perhaps due to re-arrangement of grains in the metal or soil. In a porous medium, elastic or plastic deformation will produce a change in pore volume. A change in pore volume will significantly influence the pore pressure.
Several options are available in a standard reservoir simulator to model compaction of the rock. These options are generally presented as tabulated compaction curves as a function of pore pressure. Most rocks will compact to some extent as the stress on the rock is increased and when the fluid pressure falls. Some rocks, typically chalks, will exhibit additional compaction when water contacts oil bearing rock, even at constant stress. This behavior could have a significant effect on the performance of a water flood as it adds significant energy to the reservoir. These tabulated compaction curves can also include hysteresis where a different stress path is taken depending on whether the pressure is increasing or decreasing. These paths are also called deflation and reflation curves. However, there is a need for a simpler, alternative method that allows coupling elastic or non-elastic change in rock pore volume to the stress calculation